The Eulerian idempotent in the lexicographic basis

Florian Schaetz, University of Luxembourg. Part of the algebra seminar series.

The Eulerian idempotent is a canonical map from the free algebra on generators x_1,...,x_n to the space of Lie words on x_1,..,x_n. Besides its importance in Lie theory, it also plays a central role in the theory of linear ODEs, due to its relation to the Magnus expansion. I will report on joint work in progress with Ruggero Bandiera (Sapienza - University of Rome), whose main goal is to establish a (to the best of our knowledge) new formula for the Eulerian idempotent. The derivation of this formula relies on the notion of, and computations within, pre-Lie algebras.

Florian Schaetz, University of Luxembourg